Displaying similar documents to “Collapsing algebras and Suslin trees”

Continuous tree-like scales

James Cummings (2010)

Open Mathematics

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Answering a question raised by Luis Pereira, we show that a continuous tree-like scale can exist above a supercompact cardinal. We also show that the existence of a continuous tree-like scale at ℵω is consistent with Martin’s Maximum.

A tree axiom.

Kurepa, Đuro (1985)

Publications de l'Institut Mathématique. Nouvelle Série

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The Tree Property at ω₂ and Bounded Forcing Axioms

Sy-David Friedman, Víctor Torres-Pérez (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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We prove that the Tree Property at ω₂ together with BPFA is equiconsistent with the existence of a weakly compact reflecting cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a weakly compact cardinal. Similarly, we show that the Special Tree Property for ω₂ together with BPFA is equiconsistent with the existence of a reflecting Mahlo cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a Mahlo...